What is it?
Is there a picture we can see? Why controversial?
I, too, was raised with this sensibility when among a small, modest group. One would remove one's glove as it's considered rude to take someone's hand gloved.
I was just thinking of one person glad-handing a large crowd. I see no virtue in doing so un-gloved.
There is also this: if someone (who has to do all the glad-handing) has a sensitivity, or a 'deformity' (perhaps a wart?) I could see wanting to use a glove as a courtesy. In any case, gloved or un-gloved, I never seek to shake a 'celebrity's' hand in a public place, unless they make the first move to do so. I've been taught it's an intrusion otherwise.
BTW I don't see much massive handshaking by royals (or celebrities). I'm trying to think when such happens. Is it a British thing? Do other royals do it?